A new narrative is emerging about the Jan 7 attack on the satirical magazine Charlie Hebdo—that it was spurred, at least in part, by a competition between two terrorist groups. The theory is that Al Qaeda instigated the attack, through its franchise in Yemen, in order to reclaim its position as terrorist top dog from the arrivistes known variously as ISIL, ISIS and the Islamic State.

But the real lesson from Paris is that the distinctions between Al Qaeda and ISIL are immaterial to self-styled jihadis.

At least one of the Kouachi brothers, gunmen in the Paris massacre, traveled to Yemen to train with Al Qaeda in the Arabian Peninsula, or AQAP, and US officials believe the attack was ordered by the group’s high command. But Amedy Coulibaly, who carried out several other attacks in conjunction with the Kouachis, including taking hostages at a kosher supermarket, had pledged loyalty to ISIL.

Al Qaeda in the Arabian Peninsula (AQAP) took responsibility on Friday for the attack on the Paris satirical magazine Charlie Hebdo. A statement provided to the Associated Press said “the leadership of AQAP directed the operations and they have chosen their target carefully.” The attack, which killed 12 people, was intended to as “revenge for the honor” of the Prophet Mohammad, the depiction of whom is forbidden by Islamic tradition. The magazine had repeatedly mocked him in cartoons.

The claim, which the unnamed spokesman said was delayed two days after Wednesday’s attack for “security reasons,” did not come as a shock. But one of the gunmen in the Charlie Hebdo attack shouted, “You can tell the media it was Al-Qaeda in Yemen” during the assault, according to a witness. And a the French news channel BFM Television reported that Said and Cherif Kouachi made the same claim in a…